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I've begun to think about the procedure to use for pairing people up for
games. Before describing the procedure, let me state its goals. One goal
is to maximize the number of games played by everyone. Short of that, to
maximize the number of people who play any game. Another goal is to
maximize the number of each player's top n choices that he gets to play.
Short of that, to keep each player's assignment of games in conformity
with his preferences as much as feasible.

Here is what I'm thinking of. I'll begin by getting a list of ranked
preferences from each person of his top n+3 games. I'll mark any game
that appears in everyone's top n games. Let's call the number of games
everyone has in their top n m. Everyone will play these games, but I
won't pair people up in them until I have paired people up for other
games. I will first pair people up for the remaining n minus m games.
Beginning with each person's top ranked unmarked game, I will try to find
a partner who also ranks that game highly. Someone who ranks a game more
highly will be favored over someone who ranks a game less highly. If an
odd number of players rank a game among their top n games, precedence will
be given to those who rank it higher. As much as possible, any player who
has ranked a game on top will be given an opponent who has ranked it among
his top n games. Whenever two people are paired up for a game, I will mark
that game in their rankings. After pairing up opponents on the basis of
top ranked games, I will repeat the procedure a rank lower, and repeat
again until every player has been paired up for n-m games. If the
procedure terminates without pairing everyone up on n-m games, I will
repeat the procedure on the unmarked games of player's who haven't yet
met their quota, but I will extend it to the full ranking. Then I will
pair everyone up on the games everyone put in their top n games, pairing
each person up with someone he hasn't already been paired up with.

If anyone would be happy to play any game among the top n, saying so will
make it a bit easier to pair everyone up for games they will be happy
playing. If anyone ends up unhappy with his assignment of games, he can go
read Green Eggs and Ham. If anyone has a better suggestion for how to
acheive the same goals, I will be happy to hear it.